Combining an interval approach with a heuristic to solve constrained and engineering design problems

Document Type : Research Article

Authors

• D. Sharma
• S.D. Jabeen

Department of Mathematics, Birla Institute of Technology Mesra, Ranchi 835215, India,

10.22067/ijnao.2025.93363.1640

Abstract

Solving intricate constrained optimization problems with nonlinear constraints is usually difficult. To optimize the constraint and structure engineering design challenges, this work presents a novel hybrid method called SDDS-SABC, which is based on the split-detect-discard-shrink technique and the Sophisticated ABC algorithm inspired by the integration of branch and-bound-like concepts of interval analysis with heuristics, and it differs from other methods in the literature. The advantage of the SDDS process is that it shrinks the entire search region through recursive breakdown and improves computational effort to focus on subregions covering potential solutions for further decomposition. In order to identify the most promising subregion, SABC’s values are crucial in assisting in the extraction of the best solutions from the subregions. Until the region shrinks to a nominal width that represents the global or nearly global solution(s) to the optimization problem, both SDDS and SABC are successively repeated. The selection and rating criteria are used to support positive decision-making, with the mindset of removing the subregion containing the unpromising solution(s). Simultaneously, the subregion exhibiting a viable solution is acknowledged as the present shrink region in anticipation of a subse-quent split. We present a new initialization technique for food sources in the SABC algorithm, called the quasi-random sequence-based Halton set, which outperforms the current initialization procedure. Create a composite strategy that uses the employed bee phase to investigate their neighborhood while preserving their cooperative nature. In order to increase the optimiza-
tion efficiency, we also present a new dynamic penalty approach that does not rely on any additional characteristics or factors like the majority of existing penalty methods. We test the statistical validity of SDDS-SABC by applying it to engineering design problems and benchmark functions (CEC 2006). The results demonstrate that SDDS-SABC performs better than its most studied competitors and proves its viability in resolving difficult real-life problems. Additionally, the SDDS-SABC approach is appropriate and numerically stable for the optimization problems. The main innovation of the approach being described is its capacity to perform a static and better optimal solution in the majority of runs, even when the problem is excessively complex.

Keywords

• Constrained optimization
• ABC algorithm
• Dynamic penalty function
• Engineering design problem

Main Subjects

• Optimization

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